> You need to diagonalize the binary tree rather than the list of real> > numbers - and account for multiple trees representing the same> > number. Or just ignore the real number interpretation and deal with> > binary strings without regard to numbers.> > > > My many examples of diagonalization in different contexts is a model> > to do just that. It's always good to generalize.

My concern is how one shows there are countably many paths throughthe infinite nodes. I can't move to the second path though infinityuntil I've completed the first, that is unless an algorith is proposedthat lets me idenify which infinite paths I've taken without completelytaking them. I might identify a path by its representation as a rationalnumber. Unfortunately that leaves out the irrational numbers.